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CALCCCCCCCCCCC PLSSSSSSSSSSSSSS

CALCCCCCCCCCCC PLSSSSSSSSSSSSSS-example-1
User Joonho
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1 Answer

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Answer:

The speed of the particle at t = 6 is 4 units per second

Explanation:

The problem states that a particle moves along the x-axis so that at time t > 0, its position is given by x(t) = -t² + 4t + 27. We are asked to determine the speed of the particle at t = 6.

To determine the speed of the particle, we need to find the derivative of the position function x(t) with respect to time t. This derivative represents the particle's velocity v(t).

x(t) = -t² + 4t + 27

v(t) = dx/dt = -2t + 4

Now, we can plug in t = 6 into the velocity function to find the particle's speed at that time:

v(6) = -2(6) + 4 = -8 + 4 = -4

Therefore, the speed of the particle at t = 6 is 4 units per second. Since the velocity is negative, we know that the particle is moving in the negative direction along the x-axis.

User Srohde
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